What would happen if Adam and Eve did not disobey God?
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No one really knows.
If we think of Adam and Eve as archetypes or literary composites of some sort (cf. this description of C.S. Lewis's opinion), the world would likely be no different, as we each rebel against God.
If we take Adam and Eve to be historical persons, then presumably sin and the devil would continue seeking an opportunity to gain a foothold. Perhaps they dodged his wiles on many occasions before they finally fell into sin. If they had fallen later, things would be rather like they are now, I'd think. If they had persistently resisted, then they would have presumably lived in communion with God and populated the world with their righteous descendants. (On this, compare Lewis's retelling of Eden in Perelandra, the second book in his space trilogy.)
Excursus: There is a hidden premise in some Christian literature that the new heavens and the new earth are about the same as Eden, maybe a bit better in some ways, but I don't think this is necessarily so. (I don't want to turn this into a debate about creationism, but I tend to think that there was animal death before the fall, including predation, and the new earth will apparently not be like that.) In my view, it's not so much a return to what is best as a progression toward it. God is making a good world even better. Polkinghorne suggests the laws of physics on the new earth will be different, such that things don't tend toward chaos and decay.